1. Prove the identity cos (x+(y-pi/2)) = sin (x+y)

2. Prove the identity: (5 csc^2 x+4 csc x-1 / cot ^2 x) = (5 csc x-1 / csc x-1)

3. Prove the identity: cos4u = (cos^2 2u) - (sin^2 2u)

please help, thank you!

Here are some hints:

1. If you substitute w for the quantity x+y, you get:

cos(w-Π/2) = sin(w)

That should be pretty easy to prove.

2. Whenever you're asked to prove something involving cotangent, secant, or cosecant, it's almost always a good idea to substitute the primitive functions involving sine and cosine.

3. Recall that cos(A+B) = cos(A)cos(B)-sin(A)sin(B). From this you can see that cos(2w) = cos(w+w) = cos^2(w) - sin^2(w).